CN113820052B - Methods for the Characterization of Stress in Dielectric Materials - Google Patents

Abstract

A method for characterizing stress in a dielectric material, comprising: the source terahertz wave is subjected to first modulation by parallel modulation, first front polarization modulation and focusing modulation, passes through a region of the sample, and is received as a first signal by parallel modulation, first rear polarization modulation and focusing modulation; performing second modulation on the source terahertz wave through parallel modulation, second front polarization modulation and focusing modulation, enabling the source terahertz wave to pass through the region of the sample along the same direction of the terahertz wave after first modulation, and receiving the source terahertz wave as a second signal through the parallel modulation, second rear polarization modulation and focusing modulation; the difference in amplitude of the first signal and the second signal is calculated to obtain the direction of the two principal optical axes in the region and the refractive index difference in the directions of the two principal optical axes to characterize the intensity of the principal stress difference in the region and its direction.

Description

Methods for Characterizing Stress in Dielectric Materials

Technical Field

The invention belongs to the technical field of material testing and characterization, and in particular relates to a method for characterizing stress in a dielectric material.

Background Art

In terms of measuring stress in light-opaque media, the existing technology is limited to single-point measurement due to its complex experimental steps and difficulty in obtaining full-field stress, thus making it difficult to achieve rapid full-field measurement.

During material processing and use, the internal stress of the material is one of the factors that lead to material failure and damage, especially in multi-layer bonding structures. Using a "polarimeter" to observe transparent materials can intuitively obtain the magnitude and direction of internal stress, but this method cannot be used to obtain the internal stress of opaque materials. The internal stress of opaque materials can be obtained by the pinhole method, but this is a lossy method.

Terahertz waves have good permeability for most dielectric materials, so a non-destructive testing method for measuring the internal stress of opaque dielectric materials can be established based on terahertz waves. In recent years, due to the trend of miniaturization and low cost of terahertz systems, more and more industrial and civilian product lines are using terahertz imaging systems to complete rapid non-destructive testing. Terahertz non-destructive testing is widely used in the detection of plastic materials, ceramic materials, and semiconductor materials. When plastic materials are subjected to load and strain, they change from isotropic to anisotropic and show birefringence to light. The internal stress of opaque plastic materials can be measured by terahertz waves. Ceramic-based composites are often used to manufacture thermal barrier coatings on the surface of aircraft engine blades. Terahertz waves can penetrate thermal barrier coatings and detect the thickness of various components inside the coating; its internal stress can also be measured by terahertz waves. Stress and strain in semiconductors can improve chip performance. For example, strained silicon technology physically stretches or compresses silicon crystals, thereby increasing carrier mobility and enhancing transistor performance. Stress in semiconductors can also be measured by terahertz waves.

Therefore, it is urgent to propose a method that can quickly measure the stress at each point in the opaque electrolyte sample. On the one hand, it places high demands on the measurement efficiency and the amount of calculation cannot be large, otherwise it is difficult to obtain the full-field stress distribution by fast point-by-point scanning; at the same time, it also places high demands on the measurement accuracy and cannot cause damage to the sample. At present, there is no test or characterization method that can meet the above requirements of fast, non-destructive, and accurate.

Summary of the invention

In order to partially solve the above technical problems to a certain extent, the present invention proposes a method for characterizing stress in a dielectric material, which is characterized by comprising: step a. performing a first modulation on a source terahertz wave through parallel modulation, a first front polarization modulation, and a focusing modulation, and causing the source terahertz wave to pass through an area of a sample and then be received as a first signal through parallel modulation, a first rear polarization modulation, and a focusing modulation; step b. performing a second modulation on the source terahertz wave through parallel modulation, a second front polarization modulation, and a focusing modulation, and causing the source terahertz wave to pass through the above area of the sample in the same direction as the terahertz wave after the first modulation and then be received as a second signal through parallel modulation, a second rear polarization modulation, and a focusing modulation; step c. calculating the amplitude difference between the first signal and the second signal, thereby obtaining the directions of the two main optical axes in the area and the refractive index difference in the directions of the two main optical axes, so as to characterize the intensity and direction of the principal stress difference in the area; wherein the modulation directions of the first front polarization modulation and the first rear polarization modulation are orthogonal to each other, and the modulation directions of the second front polarization modulation and the second rear polarization modulation are also orthogonal to each other.

Furthermore, the polarization directions of the first front polarization modulation and the second front polarization modulation are different.

Furthermore, both step a and step b are performed in a dark field environment.

Furthermore, the source terahertz wave is a terahertz wave emitted by a time-domain terahertz system, and its frequency is 0.2-3 THz.

Furthermore, the area is a circular area with a diameter not exceeding 3mm-7mm.

Furthermore, the principal stress difference in the area of the sample is Δσ=Δn/C, wherein Δσ is the principal stress difference between the first principal stress direction and the second principal stress direction, Δn is the refractive index difference in the directions of the two principal optical axes, and C is the stress optical coefficient of the material under the action of the terahertz wave, wherein the directions of the two principal stresses are consistent with the directions of the two principal optical axes.

Furthermore, the amplitude of the electric field signal of the terahertz wave received after passing through the sample is

为前偏振调制的方向；所述的第一主应力的方向θ与主应力差Δσ为待测量，所述的穿过试样后被接收的太赫兹波的电场信号的幅值为实验测量量。Where, f is the frequency of the source terahertz wave, d is the thickness of the specimen, c is the speed of light, and θ is the direction of the first principal stress in the specimen.

is the direction of the front polarization modulation; the direction θ of the first principal stress and the principal stress difference Δσ are to be measured, and the amplitude of the electric field signal of the terahertz wave received after passing through the sample is the experimental measurement quantity.

Further, when the first polarization modulation direction is 0 and the second polarization modulation direction is π/4, the amplitude of the first signal is A ₁ , the amplitude of the second signal is A ₂ , and the (first) principal stress direction θ is

并且所述主应力差为

And the principal stress difference is

或

or

求得。Alternatively, the principal stress difference may be passed through.

To obtain.

Further, under the action of the terahertz wave, the stress optical coefficient C of the material can be determined by table lookup or calibration experiment; or, the stress optical coefficient C of the material is measured by the following calibration experiment: step a. modulating the source terahertz wave through parallel modulation, polarization modulation before calibration, and focusing modulation, and making it pass through an area of the sample and then be received as a calibration signal through parallel modulation, polarization modulation after calibration, and focusing modulation; step b. performing the calibration measurement described in step a on a specimen in an area with known stress distribution, wherein the area with known stress distribution is a pure bending area under four-point bending loading or a uniform stress area under tensile loading; step c. calculating the amplitude difference of the calibration signal, thereby obtaining the directions of the two main optical axes in the area and the refractive index difference in the directions of the two main optical axes, and calculating the stress optical coefficient C of the material in combination with the known stress distribution described in step b; wherein the modulation directions of the polarization modulation before calibration and the polarization modulation after calibration are orthogonal to each other, and the polarization modulation before calibration is 45° with the horizontal direction.

Further, the known principal stress difference Δσ, the first principal stress direction θ and the electric field signal A of the received terahertz wave are obtained, and the stress optical coefficient C is

The beneficial effects of the present invention include but are not limited to: this method, device and system are suitable for measuring the internal stress field in various dielectric materials. This method is aimed at the problem of characterizing the internal stress of dielectric materials, and provides a new type of non-destructive and non-contact detection method for obtaining the internal stress field of the material. This method can conveniently obtain the stress field information inside the material, including the distribution of the principal stress difference and the distribution of the first principal stress. The principal stress difference is one of the important criteria for the failure behavior of the material. Based on the distribution of the principal stress difference, the specific location where the stress concentration phenomenon occurs inside the material can be predicted. More importantly, this method is a qualitative and quantitative characterization method. The size of the principal stress difference can verify whether the design of the specific structure is reasonable, whether the specific parts are qualified, and whether it is safe under specific service adjustments. The principal stress direction is of great significance to the design of the structure, especially the design optimization of fiber-reinforced materials. This method can also specifically detect whether the fiber reinforcement direction arrangement of the material is reasonable.

BRIEF DESCRIPTION OF THE DRAWINGS

Hereinafter, some specific embodiments of the present invention will be described in detail in an exemplary and non-restrictive manner with reference to the accompanying drawings. The same reference numerals in the accompanying drawings indicate the same or similar components or parts. It should be understood by those skilled in the art that these drawings are not necessarily drawn to scale.

FIG1 shows the basic structure and composition of a polarization time-domain terahertz system according to an embodiment of the present invention;

FIG2 shows polarization directions and principal stress directions, including a first polarization direction and a second polarization direction;

FIG3 shows the main function units of the four-point bending loading test device used in an embodiment of the present invention;

FIG4 shows a top view and a side view of a specimen subjected to four-point bending loading according to an embodiment of the present invention, where ROI is a measurement area;

FIG5 shows the terahertz signals of six measuring points in the ROI region of a sample subjected to four-point bending loading and the principal stress differences of the corresponding points according to an embodiment of the present invention, so as to reflect the changes of the terahertz signals under different stresses;

FIG6 shows the amplitude distribution of the terahertz wave signal in the ROI area of the sample subjected to four-point bending loading according to an embodiment of the present invention, that is, the difference between the peak value and the valley value of the terahertz wave signal;

FIG7 shows a fitting line for representing the stress optical coefficient obtained by fitting the measured refractive index difference and the calculated principal stress difference, and the refractive index difference and the principal stress difference at different points;

FIG8 shows an experimental device for measuring or calibrating the optical stress coefficient of a sample according to another embodiment of the present invention - a radial compression disk test experimental device;

FIG9 shows the loading condition of a disk-shaped sample and the ROI test area when an experimental device for measuring or calibrating the optical stress coefficient of a sample according to another embodiment of the present invention is in operation;

FIG. 10 (a) and (b) respectively show the full-field distribution of the analytical solution of the principal stress direction in the test area of the radially compressed disk when loaded (i.e., the analytical solution of the principal stress direction at each point) and the corresponding analytical solution of the principal stress difference according to an embodiment of the present invention;

图11b中

FIG. 11(a) and (b) respectively show the amplitude (distribution) of the terahertz wave signal passing through different points in the test area when the radially compressed disk is loaded according to an embodiment of the present invention, wherein FIG. 11a

In Figure 11b

FIG. 12 (a) and (b) respectively show the full-field distribution of the test results of the principal stress direction of the radially compressed disk in the test area when loaded, calculated by the terahertz test method of the embodiment of the present invention combined with the measured optical stress coefficient (i.e., the experimental solution of the principal stress direction at each point) and the corresponding experimental solution of the principal stress difference;

(a) and (b) in FIG. 13 respectively show a comparison between an experimental solution calculated by the terahertz testing method according to an embodiment of the present invention combined with the measured optical stress coefficient and a theoretical solution.

DETAILED DESCRIPTION

The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It will be appreciated that the specific embodiments described herein are only used to explain the relevant inventions, rather than to limit the invention. It should also be noted that, for ease of description, only the parts related to the invention are shown in the accompanying drawings. It should be noted that, in the absence of conflict, the embodiments in this application and the features in the embodiments may be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

It should be noted that the embodiments and features in the embodiments in this application can be combined with each other without conflict. In addition, it should be noted that the terms used in this application such as front, back, up, down, left, right, top, bottom, front, back, horizontal, vertical, etc. to indicate directions are only for the convenience of description to help understand the relative position or direction, and are not intended to limit the orientation of any device or structure.

First, it should be noted that, according to the embodiment of the present invention, only the calculation of the refractive index difference between the two principal stress directions (two principal optical axis directions) can characterize the magnitude of the principal stress directions and their differences at different positions of the sample to be tested (qualitative rather than precise quantitative), and the meaning of "characterization" here is to roughly estimate the stress/stress difference distribution, which is very efficient. However, it should be understood that the present application is not limited in this respect.

Further, as shown in FIG1 , a polarization sensitive THz-TDS system/device 100 for testing a dielectric material sample 105 includes a transmitting antenna 109, a first lens 108, a first polarizer 107, a second lens 106, a third lens 104, a second polarizer 103, a fourth lens 102, and a receiving antenna 101, as well as a loading device 110 for performing four-point bending loading on the sample 105. The loading device 110 includes a loading frame 20, a loading seat fixture 201, a fixed seat fixture 202, a loading seat 203, a fixed seat 204, and a force sensor 205 as shown in FIG3 to achieve four-point bending loading of the rectangular sample 105 and measure the loading force. In view of the fact that the four-point bending experiment and related devices are conventional technical means and common devices in experimental mechanics, the structure and operation method thereof will not be described in detail in this disclosure. However, it should be understood that the present application is not limited in this respect.

It should be noted that the experiment according to the embodiment of the present invention is generally carried out in a dark field environment, which means that there is no terahertz emission source other than the transmitting antenna 109 in the environment, and the terahertz signal amplitude of the terahertz wave finally received by the receiving antenna 101 from the transmitting antenna 109, the first lens 108, the first polarizer 107, the second lens 106, the third lens 104, the second polarizer 103, and the fourth lens 102 is low and close to the oscillation amplitude of the noise. It should be noted that the terahertz wave described here has not been modulated by the stress test piece 105. However, it should be understood that the present application is not limited in this respect.

Further, the source terahertz wave emitted by the transmitting antenna 109 is divergent, and the first lens 108 formed as a convex lens performs a first parallel modulation on it so that it is modulated into a parallel light beam, and then enters the first polarizer 107, and then is modulated by the second lens 106 formed as a convex lens to form a focused light beam, and then enters an arbitrary area of the sample 105 in a four-point bending loading state. After the light beam (i.e., the terahertz wave) passes through the sample 105, it is modulated by the third lens 104 formed as a convex lens to form a parallel light beam, and then passes through the second polarizer 103 for a second polarization modulation, and then passes through the fourth lens 102 formed as a convex lens to be focused and modulated, and then is received by the receiving antenna 101 as a first signal. It should be noted that in the above-mentioned measuring device and measuring process, the polarization directions of the first polarizer 107 and the second polarizer 103 are orthogonal to each other. However, it should be understood that the present application is not limited in this regard.

Subsequently, the polarization direction of the first polarizer 107 is adjusted to be different from the original polarization direction, and the polarization direction of the second polarizer 103 is adjusted to be orthogonal to the polarization direction of the adjusted first polarizer 107, and then the above test process is repeated so that the incident light still passes through the same area as the first test, and the signal received by the receiving antenna 101 after the second test is recorded as the second signal. However, it should be understood that the present application is not limited in this respect.

In the above system, the terahertz wave (light beam) is emitted and received by two rotatable photosensitive antennas, and the polarization directions of the two antennas are set to be orthogonal. The purpose of setting the first polarizer 107 and the second polarizer 103 is partly to obtain a higher extinction rate, and their polarization directions are set to be consistent with the transmitting antenna 109 and the receiving antenna 101, that is, the polarization direction of the first polarizer 107 is consistent with the polarization direction of the transmitting antenna 109, and the polarization direction of the second polarizer 103 is consistent with the polarization direction of the receiving antenna 101. The role of the second lens 106 is to focus the terahertz wave in the form of a spot on and pass through the sample 105. The diameter of the spot is about 5mm. The high-reliability frequency range of the above system is 0.2~2.5THz. In fact, the spot area formed on the surface of the specimen after the terahertz wave is focused and modulated; due to the wavelength and technical limitations of the terahertz wave, the spot formed by the far-field terahertz wave focusing through the lens is about 3mm-7mm, preferably 4mm-6mm, and further preferably 5mm. Therefore, the field information of a larger area can be obtained by scanning and imaging point by point through a two-dimensional displacement platform. It can be seen that another technical advantage (beneficial effect) of the present invention using the time-domain terahertz system is that its measurement field range is large.

In addition, the loading device 110 is a device capable of four-point bending loading and uniaxial compression loading as shown in FIG3 , and is equipped with a sensor 205 to measure the value of the loading force, the maximum measurement value of which is 2000 N, and the test accuracy is 0.6 N, wherein the driving device for loading is two stepping motors not shown, the maximum scanning range of which is 50 mm×50 mm, and the repeatability accuracy is 2 μm. However, it should be understood that the present application is not limited in this respect.

The propagation of terahertz waves can be represented by the Jones Matrix, and the electric field signal of the polarized terahertz wave emitted by the transmitting antenna can be expressed as

为偏振方向与水平方向之间的夹角，δ₀为太赫兹波的初始相位。Where f and t are frequency and time respectively,

is the angle between the polarization direction and the horizontal direction, and δ ₀ is the initial phase of the terahertz wave.

After the terahertz wave passes through the first polarizer 107, the loaded sample 105 and the second polarizer 103 in sequence, the electric field signal of the terahertz wave finally received by the receiving antenna 101 can be expressed as:

in,

和矩阵

为第一偏振镜107和第二偏振镜103的琼斯矩阵，体现第一偏振镜107和第二偏振镜103对太赫兹波信号的影响(本公开中太赫兹、太赫兹波、太赫兹光波等近义词如未特别释义具有相同含义)，J_θ为受到加载作用的试样的琼斯矩阵，体现加载作用及所产生的应力对太赫兹波的影响，θ为第一主应力方向，向量R代表太赫兹接收天线，其仅能够接收所述电场信号中沿

方向偏振的信号部分。然而，应该理解的是，本申请在此方面不受限制。matrix

and matrix

is the Jones matrix of the first polarizer 107 and the second polarizer 103, reflecting the influence of the first polarizer 107 and the second polarizer 103 on the terahertz wave signal (the synonyms such as terahertz, terahertz wave, terahertz light wave, etc. in the present disclosure have the same meaning if not specifically explained), J _θ is the Jones matrix of the sample under loading, reflecting the influence of the loading and the stress generated on the terahertz wave, θ is the first principal stress direction, and the vector R represents the terahertz receiving antenna, which can only receive the electric field signal along the

However, it should be understood that the present application is not limited in this regard.

Figure 2 shows the polarization direction and the principal stress direction. Combining Formula 1 and Formula 2, E ₁ can be simplified to:

When the terahertz wave passes through the loaded sample 105, it is disassembled into two polarized terahertz waves under the action of stress birefringence. The different propagation speeds cause a phase difference between the two polarized terahertz waves. After both polarized terahertz waves pass through the sample, they will be synthesized into a terahertz signal _E1 after passing through the second polarizer 103. The amplitude of _E1 can be expressed as:

Among them, δ ₁ -δ ₂ is the phase difference caused by stress between the two main optical axes. When the thickness d of the sample is constant, δ ₁ -δ ₂ can be expressed by the formula:

Where f is the frequency of the terahertz wave, c is the speed of light. Δn is the refractive index difference between the two main optical axes caused by stress birefringence, which can be expressed as

Δn＝C·Δσ (10)

和π/4时的穿过试样105的太赫兹波的幅值A，则第一主应力方向θ和主应力差Δσ可以通过下式(11)和(12)计算：Where C is the stress optical coefficient, and the principal stress difference Δσ = σ ₁ -σ ₂ . Combining the above formulas, it can be seen that the amplitude A contains the information of the first principal stress direction θ and the principal stress difference Δσ. Therefore, the two measurements of the amplitude A are necessary and sufficient to solve the equation with two unknowns θ and Δσ.

and the amplitude A of the terahertz wave passing through the sample 105 at π/4, the first principal stress direction θ and the principal stress difference Δσ can be calculated by the following equations (11) and (12):

时的幅值A也可以计算出主应力差ΔσSimilarly, by calculating

The amplitude A at the time can also be used to calculate the principal stress difference Δσ

为不同值时的多组主应力Δσ，并对主应力差取平均以获得更精确的最终结果。To obtain more precise results, measure

For different values of , multiple sets of principal stresses Δσ are obtained, and the principal stress differences are averaged to obtain a more accurate final result.

Next, in order to further accurately obtain the principal stress difference through the refractive index difference between the principal optical axes, the stress optical coefficient that has been recorded can be obtained by looking up a table or the stress optical coefficient C of different samples can be measured by calibration experiments. However, it should be understood that the present application is not limited in this respect.

One embodiment of measuring the stress optical coefficient C of a material sample

The sample used in this embodiment is made of PTFE (Poly tetra fluoroethylene, abbreviated as PTFE), and a four-point bending test is used to determine its stress optical coefficient C. The dotted line portion in Figure 4 shows the measurement area (i.e., ROI area), the size of which is 28mm×2mm, and the scanning step length is 0.5mm. The direction of the principal stress in this area is unchanged, but the magnitude varies.

Based on the theory of elastic mechanics, the principal stress difference along the x-axis in the ROI region can be calculated by the following formula (14):

Wherein, l, d and h are the geometric dimensions of the bent sample 105 shown in FIG4 , p is the static pressure, and the values of the relevant parameters of the sample are listed in Table 1. It can be seen from the above formula (14) that the principal stress difference Δσ is proportional to the x-coordinate value. In the measurement area, the first principal stress direction θ is always π/2. According to the stress optical effect, the stress will modulate the terahertz time domain signal passing through the sample. FIG5 shows the experimental data of the bent sample, in which the terahertz time domain signal is measured at 6 points along the x-axis direction, with an interval of 2.5 mm between each point. The waveforms of the terahertz waves passing through these points are shown in FIG5 , and it can be seen that the amplitude of the signal is obviously modulated by the stress. Next, the terahertz time domain signals of all points in the measurement area are measured, and their amplitudes are calculated by the peak-trough difference, that is, the difference between the maximum and minimum values of the waveform. FIG6 shows the distribution of the amplitude in the measurement area, and it can be seen that the amplitude increases from left to right due to the continuous increase of the principal stress difference Δσ. However, it should be understood that the present application is not limited in this regard.

Table 1. Four-point bending test parameters

设置为π/4，鉴于A|_φ＝π/4可以在弯曲实验中测得(即φ＝π/4时太赫兹波穿过试样后的信号的幅值)，由应力双折射所产生的折射率差Δn能够得以确定，在上述公式(10)中，应力光学系数C为折射率差Δn与主应力差Δσ之间的比值，图7示出了根据本发明实施例的实验测得的Δn和Δσ的结果，相关性系数C根据实验测定的结果通过线性拟合得到，所使用的PTFE材料的最终测得的应力光学相关性系数C为-2.4×10^-10Pa^-1。然而，应该理解的是，本申请在此方面不受限制。In the bending experiment according to the embodiment of the present invention, the polarization direction angle of the first polarizer 107 is

Set to π/4, considering that A| _φ＝π/4 can be measured in a bending experiment (i.e., the amplitude of the signal after the terahertz wave passes through the sample when φ＝π/4), the refractive index difference Δn generated by stress birefringence can be determined. In the above formula (10), the stress optical coefficient C is the ratio between the refractive index difference Δn and the principal stress difference Δσ. FIG7 shows the experimentally measured results of Δn and Δσ according to an embodiment of the present invention. The correlation coefficient C is obtained by linear fitting based on the experimentally measured results. The final measured stress optical correlation coefficient C of the PTFE material used is -2.4×10 ^-10 Pa ^-1 . However, it should be understood that the present application is not limited in this regard.

After the stress optical coefficient C is measured, it can be used to calculate the stress field from the amplitude field through formulas (10)-(12), so as to quickly and accurately calculate the stress distribution of the whole field of the sample to be tested. However, it should be understood that the present application is not limited in this respect.

Example 2 of Determining the Stress-Optical Coefficient C of a Material Sample

The sample 30 used in this embodiment of the present invention is made of PTFE, and a radial compression disk test is used to determine its stress optical coefficient C.

FIG8 shows the core unit of the experimental device used in the test, including a loading frame 40, a fixed seat 404, a fixed seat fixture 402, a force sensor 405, a sample 30, a loading seat 403, etc., wherein the sample 30 is loaded by the loading seat fixture 401 and the fixed seat fixture 402, and the force sensor 405 is used to measure the size of the loading pressure load p. The red line portion in FIG9 shows the measurement area, which is a circle with a diameter of 45 mm and a scanning step length of 0.5 mm. However, it should be understood that the present application is not limited in this regard.

Table 2. Experimental parameters of radial compression disk

Based on the theory of elasticity, the analytical solution to the stress field on a radially compressed disk can be expressed as

Where p is the applied load, r and d are the radius and thickness of the specimen. The first principal stress direction θ and the principal stress difference Δσ can be calculated as:

10a and b show the analytical solutions for the first principal stress direction θ and the principal stress difference Δσ of the radially compressed disk specimen 30.

和

的条件下，扫描对径受压圆盘试样30上的各个点的太赫兹信号，在扫描过程中加载是静态的。图11a和b给出了不同设置下测量到的穿过圆盘试样30的太赫兹波的振幅分布。若假设已知C的值，则根据公式(11)-(13)就可以计算第一主应力方向θ和主应力差Δσ。为了确定C的值，定义误差函数H(C)的表达式为The experiment of terahertz penetrating the sample 30 in the time-domain terahertz system in the above embodiment was repeated, and the distribution of the amplitude A of the terahertz wave was measured when the polarization angle of the polarizer was set to different angles;

and

Under the condition of , the terahertz signal of each point on the radially compressed disk sample 30 is scanned. The load is static during the scanning process. Figures 11a and b show the amplitude distribution of the terahertz wave passing through the disk sample 30 measured under different settings. If it is assumed that the value of C is known, the first principal stress direction θ and the principal stress difference Δσ can be calculated according to formulas (11)-(13). In order to determine the value of C, the expression of the error function H(C) is defined as

Wherein, Δσ _i is the experimental result calculated by formula (11)-(13), Δσ _i0 is the analytical solution of the principal stress difference given by formula (17), and n is the number of measurement points in the experimental area. When the error function reaches the minimum value, C at this time is the stress optical coefficient of the material. The stress field is then calculated from the amplitude field by formula (11)-(13), thereby obtaining a stress distribution diagram of the entire field, as shown in FIG12. However, it should be understood that the present application is not limited in this respect.

Comparing the actual experimental measurement results shown in Figure 12 with the theoretical analytical solution shown in Figure 10, it can be found that the measured values of the distribution of the principal stress difference and the principal stress direction are close to the theoretical values, and there is a large error only at the mutation point of the principal stress direction. This error is due to the large size of the terahertz wave focusing spot of this method, and the characterization of the stress field mutation point is limited by the spatial resolution limit. It can be seen that the experimental measurement values are basically consistent with the theoretical values, which can verify the effectiveness of this method.

Furthermore, as shown in Figures 13a and b, the test results obtained by the terahertz wave penetration amplitude characterization method for the diameter original disk experiment according to the second embodiment of the present invention have a small average error with the theoretical analytical solution, and the analytical solution is obtained under ideal conditions. The actual test situation is affected by many external factors such as temperature field, magnetic field/electric field, humidity field, etc. It can be considered that the experimental results are closer to the actual situation. It can be seen that the method, system and/or device of the present application has practicality and industrial application value.

The above description is only a preferred embodiment of the present application and an explanation of the technical principles used. Those skilled in the art should understand that the scope of the invention involved in the present application is not limited to the technical solution formed by a specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the inventive concept. For example, the above features are replaced with the technical features with similar functions disclosed in this application (but not limited to) by each other.

Claims (9)

1. A method for characterizing stress in a dielectric material, comprising: Step a. performing a first modulation on the source terahertz wave through parallel modulation, first front polarization modulation, and focus modulation, and allowing the wave to pass through an area of the sample and then be received as a first signal through parallel modulation, first rear polarization modulation, and focus modulation; Step b. performing a second modulation on the source terahertz wave through parallel modulation, a second front polarization modulation, and a focus modulation, and allowing the source terahertz wave to pass through the above-mentioned area of the sample in the same direction as the first modulated terahertz wave, and then undergo parallel modulation, a second rear polarization modulation, and a focus modulation to be received as a second signal; Step c. calculating the amplitude difference between the first signal and the second signal, thereby obtaining the directions of the two principal optical axes in the region and the refractive index difference in the directions of the two principal optical axes, so as to characterize the intensity and direction of the principal stress difference in the region; wherein the modulation directions of the first front polarization modulation and the first rear polarization modulation are orthogonal to each other, and the modulation directions of the second front polarization modulation and the second rear polarization modulation are also orthogonal to each other; The polarization directions of the first front polarization modulation and the second front polarization modulation are different. 2. The characterization method according to claim 1, characterized in that both step a and step b are performed in a dark field environment. 3. The characterization method according to claim 1, characterized in that the source terahertz wave is a terahertz wave emitted by a time-domain terahertz system, and its frequency is 0.2-3 THz. 4. The characterization method according to claim 1, characterized in that the area is a circular area with a diameter of 3 mm-7 mm. 5. The characterization method according to claim 1 is characterized in that the principal stress difference of the area of the sample is Δσ=Δn/C, wherein Δσ is the principal stress difference between the first principal stress direction and the second principal stress direction, Δn is the refractive index difference in the directions of the two principal optical axes, and C is the stress optical coefficient of the material under the action of the terahertz wave, wherein the directions of the two principal stresses are consistent with the directions of the two principal optical axes. 6. The characterization method according to any one of claims 1 to 5, characterized in that the amplitude of the electric field signal of the terahertz wave received after passing through the sample is

Where, f is the frequency of the source terahertz wave, d is the thickness of the specimen, c is the speed of light, and θ is the direction of the first principal stress in the specimen.

is the direction of the front polarization modulation; the direction θ of the first principal stress and the principal stress difference Δσ are to be measured, and the amplitude of the electric field signal of the terahertz wave received after passing through the sample is the experimental measurement quantity. 7. The characterization method according to claim 6, characterized in that, when the first polarization modulation direction is 0 and the second polarization modulation direction is π/4, the amplitude of the first signal is A ₁ , the amplitude of the second signal is A ₂ , and the direction θ of the first principal stress is

And the principal stress difference is

or

Alternatively, the principal stress difference can be obtained by

To obtain. 8. The characterization method according to any one of claims 5 to 7, characterized in that the stress optical coefficient C of the material under the action of the terahertz wave can be determined by looking up a table or a calibration experiment; or, the stress optical coefficient C of the material is measured by the following calibration experiment: Step a. modulating the source terahertz wave through parallel modulation, polarization modulation before calibration, and focusing modulation, and passing through an area of the sample, and then receiving it as a calibration signal through parallel modulation, polarization modulation after calibration, and focusing modulation; Step b. performing the calibration measurement described in step a on a specimen in an area with known stress distribution, wherein the area with known stress distribution is a pure bending area under four-point bending loading or a uniform stress area under tensile loading; Step c. Calculate the amplitude difference of the calibration signal to obtain the directions of the two main optical axes in the region and the refractive index difference in the directions of the two main optical axes, and calculate the stress optical coefficient C of the material in combination with the known stress distribution described in step b; The modulation directions of the polarization modulation before calibration and the polarization modulation after calibration are orthogonal to each other, and the polarization modulation before calibration is at 45° with the horizontal direction. 9. The characterization method according to claim 8, characterized in that the stress optical coefficient C is obtained by using the known principal stress difference Δσ, the first principal stress direction θ and the electric field signal A of the received terahertz wave.

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